After all, the National Rifle Association, which had a representative in the room Jan. 10, blasted the session immediately after, saying it was more about attacking the Second Amendment than about keeping children safe.

But another gun rep in the room, Richard Feldman, president of the Independent Firearm Owners Association, reports progress. He has received word from the vice president’s office that President Obama’s FY 2014 budget will double funding for the National Integrated Ballistic Information Network. NIBIN is a ballistic imaging system that enables the capture and comparison of images of bullets and cartridges to aid in solving crimes and establishing links between crimes.

In the 2014 budget, funding for NIBIN will rise by $24 million, to $50 million – a tiny sum in the context of the federal budget, but still meaningful to law enforcement.

“That budget request will allow ATF [the Bureau of Alcohol, Tobacco, Firearms, and Explosives] to make necessary upgrades to equipment, assist state and local law enforcement with input and analysis of ballistics information, and train state and local partners,” Mr. Biden’s office told Mr. Feldman in an email.

Feldman says he pushed for more NIBIN funding in the Jan. 10 meeting with Biden.

“This tells me they listened,” he says.

"We still have some major disagreements,” Feldman adds, “but we shouldn't allow the things that divide us from moving forward on the many issues we agree upon, this [NIBIN] being an important one.”

Meanwhile, on Capitol Hill, discussion of the next steps to take to combat gun violence continues. On Wednesday afternoon, the Congressional Gun Violence Task Force will hold a hearing, with testimony from sportsmen, gun-rights advocates, law enforcement, and mental-health professionals.

According to Rep. Mike Thompson (D) of California, chairman of the task force, the hearing will focus on steps Congress can take to keep guns out of the hands of people who should not have them, while protecting the rights of responsible, law-abiding citizens.

Gun violence became a top concern for the Obama administration after a massacre of schoolchildren last month in Newtown, Conn. Obama mentioned Newtown in his inaugural address Monday, as he went through the priorities of his second term. On Tuesday, three people were wounded in a shooting at a community college near Houston.